2004 Neon shakes in reverse?

I have a 2000 neon with approx. 237,000 kms on it. The vehicle runs well overall but just recently began to shake when I put it into reverse. Once I push the gas it goes away but while my foot is on the brake it shakes very noticable. I have talked to a couple of mechanics about this problem but nobody seems to know. Any help on this would be greatly appreciated. It would also be great to go back to these two mechanics and tell them what it is, they didn't treat me very well when I ask about this. Apparently if they can't answer a question, the customer is stupid.

I am not positive on a 2000 neon, but I would imagine your reverse band needs to be adjusted. If you have a Haynes/Chiltons Manual, that should help you locate it. The band may need adjusting from time to time, and if it hasn't been done in 237,000 km's, chances are it needs it. Also check your tranny fluid leve and make sure it is topped off.

Thanks for the info, will try tomorrow and let you know how it works out. Its great to have a place to go where someone may know. Hey that rhymes!
Truly, thanks

Did transmission service which included fluid flush, replace filter and adjust bands. This did not change things but was time for the tranny service anyway. Next thing to look at is motor mounts, this is the only other thing I can think of that will cause this type of shaking. Will let you know how it goes. Thank you for your input, it is very much appreciated.